18
Chapter 1 | Functions and Graphs
x , this equation has no solutions, and therefore f has no zeros. b. The y -intercept is given by ⎛ ⎝ 0, f (0) ⎞ ⎠ = (0, 3+1). c. To graph this function, we make a table of values. Since we need x +3≥0, we need to choose values of x ≥−3. We choose values that make the square-root function easy to evaluate.
−3 −2 1
x
f ( x )
3
1
2
Table 1.2 Making use of the table and knowing that, since the function is a square root, the graph of f should be similar to the graph of y = x , we sketch the graph ( Figure 1.10 ).
Figure 1.10 The graph of f ( x ) = x +3+1 has a y -intercept but no x -intercepts.
Find the zeros of f ( x ) = x 3 −5 x 2 +6 x .
1.3
Example 1.5 Finding the Height of a Free-Falling Object
If a ball is dropped from a height of 100 ft, its height s at time t is given by the function s ( t ) =−16 t 2 +100, where s is measured in feet and t is measured in seconds. The domain is restricted to the interval [0, c ], where t =0 is the time when the ball is dropped and t = c is the time when the ball hits the ground. a. Create a table showing the height s ( t ) when t = 0, 0.5, 1, 1.5, 2, and 2.5. Using the data from the table, determine the domain for this function. That is, find the time c when the ball hits the ground. b. Sketch a graph of s .
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